椭圆环面蜗杆与渐开线圆柱齿轮啮合相关理论及啮合性能研究

doi:10.3901/JME.2025.03.325

机械工程学报 ›› 2025, Vol. 61 ›› Issue (3): 325-336.doi: 10.3901/JME.2025.03.325

• 机械动力学 • 上一篇

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椭圆环面蜗杆与渐开线圆柱齿轮啮合相关理论及啮合性能研究

凌四营¹, 张衡², 杨振湘¹, 张嘉阳¹, 凌明³, 王奉涛¹

1. 汕头大学智能制造技术教育部重点实验室汕头 515063;
2. 北方华创科技集团股份有限公司北京 100015;
3. 大连理工大学微纳米技术及系统辽宁省重点实验室大连 116023

收稿日期:2024-05-07 修回日期:2024-10-28 发布日期:2025-03-12
作者简介:凌四营(通信作者)，男，1978年出生，博士，博士研究生导师，教授。主要研究方向为精密加工、精密机械设计、精密磨齿工艺及测试技术、传动机构设计与高端装备制造。E-mail:syling@stu.edu.cn
基金资助:
国家自然科学基金(52075067)和汕头大学科研启动经费(NTF23008)资助项目。

Research on the Relevant Meshing Theories and Meshing Performance of Elliptical Toroidal Worm Gears and Cylindrical Gears

LING Siying¹, ZHANG Heng², YANG Zhenxiang¹, ZHANG Jiayang¹, LING Ming³, WANG Fengtao¹

1. Key Laboratory of Intelligent Manufacturing Technology of Ministry of Education, Shantou University, Shantou 515063;
2. NAURA Technology Group Co., Ltd., Beijing 100015;
3. Key Laboratory for Mico/Nano Technology and System of Liaoning Province, Dalian University of Technology, Dalian 116023

Received:2024-05-07 Revised:2024-10-28 Published:2025-03-12

摘要/Abstract

摘要： 开环大速比高精度齿轮传动副在高端装备及精密仪器的分度系统中有重要的应用价值，但目前渐开面包络环面蜗杆(TI)传动的啮合性能受螺旋角取值的影响较大，其传动过程中存在偏载、不能全齿面参与啮合等问题，不能直接满足高端装备及精密仪器的分度精度需求。针对这些问题，首先提出一种与渐开线圆柱齿轮全齿面共轭的椭圆环面蜗杆(EI蜗杆)传动新形式，建立椭圆环面与渐开线圆柱齿轮圆柱面之间的空间位置关系，推导出椭圆环面的母线方程，基于齿轮空间共轭啮合原理建立渐开面一次包络EI蜗杆的啮合相关理论。其次通过分析EI蜗杆传动的啮合参数对瞬时接触线分布的影响规律，优化瞬时接触线在齿轮齿面上的分布区域，实现了渐开线圆柱齿轮全齿面与EI蜗杆啮合传动。最后分析EI蜗杆传动的啮合参数对诱导法曲率、润滑角、相对卷吸速度的影响。在相同参数的理想状态下，通过对比EI蜗杆与TI蜗杆传动中齿轮齿面啮合区域及啮合性能，发现：EI蜗杆传动中齿轮齿面啮合区域面积是TI蜗杆传动的5.49倍、诱导法曲率和润滑角相近、相对卷吸速度更大。因此，EI蜗杆传动具有共轭齿面间贴合程度高、接触强度大及润滑效果好的优点。研究成果为高性能蜗杆传动的设计提供了理论依据。

关键词: 椭圆环面蜗杆, 圆柱齿轮, 齿面接触线分布, 啮合性能, 全齿面啮合

Abstract: The open-loop high-speed ratio and high-precision gear drive has important application value in the indexing system of high-end equipment and precision instruments, however, the involute enveloping toroidal worm (TI worm) gearing is influenced by the value of the helix angle, and there are issues of partial load and unable to participate in meshing with whole tooth flank in the transmission process, which cannot directly meet the indexing accuracy requirements of high-end equipment and precision instruments. To address these issues, firstly, a new form of elliptic toroidal worm (EI worm) gearing conjugated with the full tooth flank of involute gear is proposed, the spatial position relationship between the elliptic toroidal surface and the cylindrical surface of involute cylindrical gear is established, the generatrix equation of elliptic toroidal surface is derived, the relevant meshing theories of primary envelope elliptic toroidal worm is studied based on the principle of spatial conjugate mesh of gears. Secondly, by analyzing the influence of the meshing parameters on the instantaneous contact line, the distribution area of the instantaneous contact line on the gear tooth flank is optimized, the whole tooth flank of the cylindrical gear meshing with EI worm is realized. Finally, the influence of the meshing parameters on the induced normal curvature, lubrication angle and relative entrainment speed is analyzed. Under the ideal condition with the same parameters, by comparing the meshing area of gear and meshing performance of EI worm gearing and TI worm gearing, it is found that the meshing area of gear in EI worm gearing is 5.49 times larger than that of TI worm gearing, the induced normal curvature and lubrication angle are similar, and the relative entrainment speed is larger, so the EI worm gearing is of high fitting degree between conjugate tooth flank, high contact strength and good lubrication effect. The research results provided theoretical basis for high-performance worm gear gearing.

Key words: elliptical toroidal worm, cylindrical gear, distribution of tooth contact line, meshing performance, whole tooth flank meshing

中图分类号:

TH132

凌四营, 张衡, 杨振湘, 张嘉阳, 凌明, 王奉涛. 椭圆环面蜗杆与渐开线圆柱齿轮啮合相关理论及啮合性能研究[J]. 机械工程学报, 2025, 61(3): 325-336.

LING Siying, ZHANG Heng, YANG Zhenxiang, ZHANG Jiayang, LING Ming, WANG Fengtao. Research on the Relevant Meshing Theories and Meshing Performance of Elliptical Toroidal Worm Gears and Cylindrical Gears[J]. Journal of Mechanical Engineering, 2025, 61(3): 325-336.

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椭圆环面蜗杆与渐开线圆柱齿轮啮合相关理论及啮合性能研究

Research on the Relevant Meshing Theories and Meshing Performance of Elliptical Toroidal Worm Gears and Cylindrical Gears

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